${\displaystyle x\in [0,1)}$

${\displaystyle f(x)={\frac {1}{\pi {\sqrt {x(1-x)}}}}}$

${\displaystyle F(x)={\frac {2}{\pi }}\arcsin \left({\sqrt {x}}\right)}$

${\displaystyle {\frac {1}{2}}}$

${\displaystyle {\frac {1}{2}}}$

${\displaystyle x\in \{0,1\}}$

${\displaystyle {\tfrac {1}{8}}}$

0

${\displaystyle -{\tfrac {3}{2}}}$

${\displaystyle \ln {\tfrac {\pi }{4}}}$

${\displaystyle 1+\sum _{k=1}^{\infty }\left(\prod _{r=0}^{k-1}{\frac {2r+1}{2r+2}}\right){\frac {t^{k}}{k!}}}$

${\displaystyle {}_{1}F_{1}({\tfrac {1}{2}};1;i\,t)}$